Question 102 of 183

A particle of mass $m$ moves in a circular orbit under the central potential field, $U\left(r\right)=\dfrac{-C}{r}$, where $C$ is a positive constant. The correct radius - velocity graph of the particle's motion is :

ABCD

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Answer: (A)

$U=-\dfrac{C}{r}$
$F=-\dfrac{dU}{dr}=-\dfrac{C}{{r}^{2}}$
$\left|F\right|=\dfrac{m{v}^{2}}{r}$
$\dfrac{C}{{r}^{2}}=\dfrac{m{v}^{2}}{r}$
${v}^{2}\propto \dfrac{1}{r}$